"Stephen Colbert is one of the most inventive and respected forces on television,” Moonves said. “David Letterman’s legacy and accomplishments are an incredible source of pride for all of us here, and today’s announcement speaks to our commitment of upholding what he established for CBS in late night.”

Added Tassler: “Stephen is a multi-talented and respected host, writer, producer, satirist and comedian who blazes a trail of thought-provoking conversation, humor and innovation with everything he touches. He is a presence on every stage, with interests and notable accomplishments across a wide spectrum of entertainment, politics, publishing and music. We welcome Stephen to CBS with great pride and excitement, and look forward to introducing him to our network television viewers in late night.”

The producers and the location for the Colbert-hosted Late Show will be determined and announced at a later date. The premiere date will be announced after Letterman determines his final broadcast. The Late Show airs weeknights at 11:35 p.m.

“Simply being a guest on David Letterman’s show has been a highlight of my career,” Colbert said. “I never dreamed that I would follow in his footsteps, though everyone in late night follows Dave’s lead.”

He added: “I’m thrilled and grateful that CBS chose me. Now, if you’ll excuse me, I have to go grind a gap in my front teeth.”

Letterman announced his retirement on his April 3 show after more than 20 years at CBS.

"The man who owns this network, LeslieMoonves, he and I have had a relationship for years and years and years, and we have had this conversation in the past, and we agreed that we would work together on this circumstance and the timing of this circumstance. And I phoned him just before the program, and I said 'Leslie, it's been great, you've been great, and the network has been great, but I'm retiring,' " Letterman told his audience.

Colbert Report, which launched in 2005, has earned an Emmy win for outstanding variety series (2013) and three Emmy wins for writing for a variety, music or comedy program (2013, 2010, 2008).

Of his replacement, Letterman said this: “Stephen has always been a real friend to me. I’m very excited for him, and I’m flattered that CBS chose him. I also happen to know they wanted another guy with glasses.”

Before that, Colbert spent eight years as a correspondent on Comedy Central’s The Daily ShowWith Jon Stewart as an on-air personality and writer of news satire. He also has written two books -- I Am America (and So Can You!) and America Again: Re-Becoming the Greatness We Never Weren’t -- and won a Grammy for spoken word for America Again earlier this year.

Colbert was recently embroiled in controversy following a racially insensitive tweet that was sent from the Comedy Central show's Twitter account.

“I am willing to show #Asian community I care by introducing the Ching-Chong Ding-Dong Foundation for Sensitivity to Orientals or Whatever,” The Colbert Report's official Twitter account posted the evening of March 27.

The joke, tweeted without context, was a reference to a bit from the March 26 episode, in which Colbert made fun of Washington Redskins owner DanSnyder's recent move to establish the Washington Redskins Original Americans Foundation in response to controversy over the team's name, which many consider to be racist. Out of context, the joke shocked and enraged Twitter users, who quickly mobilized a #CancelColbert campaign.

The Colbert Report on March 31 opened with a dream sequence featuring news reports of the outcry calling for the show to be canceled before Colbert -- dressed in Washington Redskins garb -- was wakened by B.D. Wong. Later, the satirical late-night news host didn't miss a beat when he addressed the Twitter controversy in a lengthy "Who's Attacking Me Now?" segment, which also included a rant about emojis. Twitter co-founder Biz Stone also appeared at the end of the program, to shut down @ColbertReport. (The Twitter page no longer exists.)